https://file.aiquickdraw.com/mathbot/file/1728851987406y7dszrk9.jpg

The expression in the image is as follows:

\[
(2x^2 + 12xy - 11) + (6x^2 - 2x + 4) + (-x^2 - y - 2)
\]

Now, let's simplify this expression by combining like terms.

### Step-by-step simplification:

1. Group the \(x^2\) terms:
   \[
   2x^2 + 6x^2 - x^2 = 7x^2
   \]

2. Group the \(xy\) term:
   \[
   12xy
   \]

3. Group the \(x\) terms:
   \[
   -2x
   \]

4. Group the constants:
   \[
   -11 + 4 - 2 = -9
   \]

5. Group the \(y\) term:
   \[
   -y
   \]

So, the simplified expression is:

\[
7x^2 + 12xy - 2x - y - 9
\]

Would you like further details on this process or additional clarification? Here are some related questions to consider:

1. How do you combine like terms in polynomial expressions?
2. What role do coefficients play when simplifying algebraic terms?
3. How does the distributive property help when simplifying expressions?
4. How can you factor the final expression \(7x^2 + 12xy - 2x - y - 9\)?
5. How can this expression be used in solving systems of equations?

**Tip:** Always arrange terms in descending order of their exponents to keep the expression organized.

(2x^2 + 12xy - 11) + (6x^2 - 2x + 4) + (-x^2 - y - 2)

This solution walks through the simplification of a polynomial expression by combining like terms. Learn how terms with x^2, xy, x, y, and constants are grouped and simplified. Suitable for Grades 9-11 math students.

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